df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1278, 1280, 1279, 1279, 1280
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6514278 0.3491897 0.5041809
## 1e-04 0.6514270 0.3491918 0.5041797
## 1e-01 0.6516483 0.3494942 0.5036084
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 1e-04.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2528.1
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 529.86 2526.6
## - fixed.acidity 1 530.04 2527.0
## - residual.sugar 1 530.05 2527.0
## - citric.acid 1 530.12 2527.2
## <none> 529.67 2528.1
## - pH 1 530.72 2528.6
## - free.sulfur.dioxide 1 530.76 2528.7
## - chlorides 1 534.06 2536.7
## - total.sulfur.dioxide 1 535.48 2540.1
## - sulphates 1 545.02 2562.6
## - volatile.acidity 1 561.57 2600.9
## - alcohol 1 565.36 2609.5
##
## Step: AIC=2526.55
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 530.04 2525.0
## - residual.sugar 1 530.05 2525.0
## - citric.acid 1 530.32 2525.7
## <none> 529.86 2526.6
## - free.sulfur.dioxide 1 531.03 2527.4
## - pH 1 532.24 2530.3
## - chlorides 1 534.41 2535.5
## - total.sulfur.dioxide 1 535.82 2538.9
## - sulphates 1 545.44 2561.6
## - volatile.acidity 1 562.95 2602.0
## - alcohol 1 624.15 2734.0
##
## Step: AIC=2525
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 530.27 2523.6
## - citric.acid 1 530.32 2523.7
## <none> 530.04 2525.0
## - free.sulfur.dioxide 1 531.30 2526.0
## - pH 1 534.59 2533.9
## - chlorides 1 535.38 2535.8
## - total.sulfur.dioxide 1 537.15 2540.0
## - sulphates 1 545.83 2560.5
## - volatile.acidity 1 564.01 2602.5
## - alcohol 1 624.38 2732.5
##
## Step: AIC=2523.55
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 530.49 2522.1
## <none> 530.27 2523.6
## - free.sulfur.dioxide 1 531.64 2524.9
## - pH 1 534.91 2532.7
## - chlorides 1 535.52 2534.2
## - total.sulfur.dioxide 1 537.19 2538.1
## - sulphates 1 545.87 2558.6
## - volatile.acidity 1 564.02 2600.5
## - alcohol 1 626.65 2735.1
##
## Step: AIC=2522.09
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 530.49 2522.1
## - free.sulfur.dioxide 1 532.01 2523.7
## - pH 1 535.26 2531.5
## - chlorides 1 536.20 2533.8
## - total.sulfur.dioxide 1 537.94 2537.9
## - sulphates 1 545.94 2556.8
## - volatile.acidity 1 571.78 2616.0
## - alcohol 1 628.70 2737.3
## Start: AIC=2540.79
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 534.98 2539.8
## - free.sulfur.dioxide 1 535.23 2540.4
## <none> 534.55 2540.8
## - fixed.acidity 1 535.45 2540.9
## - residual.sugar 1 535.79 2541.8
## - citric.acid 1 536.05 2542.4
## - pH 1 537.03 2544.7
## - total.sulfur.dioxide 1 541.02 2554.2
## - chlorides 1 542.79 2558.4
## - sulphates 1 559.56 2597.3
## - volatile.acidity 1 560.58 2599.7
## - alcohol 1 574.32 2630.6
##
## Step: AIC=2539.84
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 535.47 2539.0
## - free.sulfur.dioxide 1 535.77 2539.7
## - residual.sugar 1 535.79 2539.8
## <none> 534.98 2539.8
## - citric.acid 1 536.50 2541.4
## - pH 1 540.55 2551.1
## - total.sulfur.dioxide 1 541.79 2554.0
## - chlorides 1 543.63 2558.4
## - sulphates 1 559.89 2596.1
## - volatile.acidity 1 562.39 2601.8
## - alcohol 1 641.22 2769.7
##
## Step: AIC=2538.99
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 535.47 2539.0
## - residual.sugar 1 536.33 2539.1
## - free.sulfur.dioxide 1 536.34 2539.1
## - citric.acid 1 536.50 2539.4
## - total.sulfur.dioxide 1 544.02 2557.3
## - pH 1 545.46 2560.7
## - chlorides 1 545.86 2561.6
## - sulphates 1 560.93 2596.5
## - volatile.acidity 1 562.71 2600.5
## - alcohol 1 642.06 2769.4
## Start: AIC=2567.19
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 546.35 2565.8
## - residual.sugar 1 546.48 2566.1
## - density 1 546.72 2566.6
## - fixed.acidity 1 546.76 2566.7
## <none> 546.11 2567.2
## - pH 1 547.18 2567.7
## - free.sulfur.dioxide 1 548.11 2569.9
## - chlorides 1 550.70 2575.9
## - total.sulfur.dioxide 1 552.51 2580.1
## - volatile.acidity 1 567.64 2614.7
## - sulphates 1 569.33 2618.5
## - alcohol 1 580.94 2644.3
##
## Step: AIC=2565.76
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 546.68 2564.5
## - fixed.acidity 1 546.81 2564.8
## - density 1 546.95 2565.2
## <none> 546.35 2565.8
## - pH 1 547.39 2566.2
## - free.sulfur.dioxide 1 548.64 2569.1
## - chlorides 1 551.82 2576.5
## - total.sulfur.dioxide 1 553.98 2581.5
## - sulphates 1 569.47 2616.8
## - volatile.acidity 1 572.64 2623.9
## - alcohol 1 581.07 2642.6
##
## Step: AIC=2564.53
## .outcome ~ fixed.acidity + volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 546.91 2563.1
## - density 1 546.97 2563.2
## <none> 546.68 2564.5
## - pH 1 548.34 2566.4
## - free.sulfur.dioxide 1 549.26 2568.6
## - chlorides 1 552.18 2575.3
## - total.sulfur.dioxide 1 554.18 2579.9
## - sulphates 1 569.60 2615.1
## - volatile.acidity 1 573.34 2623.4
## - alcohol 1 598.73 2678.9
##
## Step: AIC=2563.06
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 546.98 2561.2
## <none> 546.91 2563.1
## - free.sulfur.dioxide 1 549.51 2567.1
## - pH 1 552.91 2575.0
## - chlorides 1 553.02 2575.3
## - total.sulfur.dioxide 1 555.25 2580.4
## - sulphates 1 569.63 2613.1
## - volatile.acidity 1 574.86 2624.8
## - alcohol 1 626.42 2734.7
##
## Step: AIC=2561.23
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 546.98 2561.2
## - free.sulfur.dioxide 1 549.61 2565.4
## - pH 1 553.03 2573.3
## - chlorides 1 553.06 2573.4
## - total.sulfur.dioxide 1 555.28 2578.5
## - sulphates 1 569.92 2611.8
## - volatile.acidity 1 575.12 2623.4
## - alcohol 1 647.06 2774.2
## Start: AIC=2516.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 524.89 2514.5
## - residual.sugar 1 524.90 2514.5
## - fixed.acidity 1 524.93 2514.6
## - citric.acid 1 525.17 2515.2
## <none> 524.80 2516.3
## - pH 1 525.89 2516.9
## - free.sulfur.dioxide 1 527.08 2519.8
## - chlorides 1 531.16 2529.7
## - total.sulfur.dioxide 1 532.44 2532.8
## - sulphates 1 544.34 2561.0
## - volatile.acidity 1 554.81 2585.4
## - alcohol 1 562.10 2602.1
##
## Step: AIC=2514.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 524.92 2512.6
## - fixed.acidity 1 524.93 2512.6
## - citric.acid 1 525.27 2513.4
## <none> 524.89 2514.5
## - pH 1 527.23 2518.2
## - free.sulfur.dioxide 1 527.26 2518.3
## - chlorides 1 531.53 2528.6
## - total.sulfur.dioxide 1 532.71 2531.4
## - sulphates 1 544.98 2560.6
## - volatile.acidity 1 556.09 2586.4
## - alcohol 1 620.45 2726.4
##
## Step: AIC=2512.59
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 524.97 2510.7
## - citric.acid 1 525.28 2511.5
## <none> 524.92 2512.6
## - pH 1 527.25 2516.2
## - free.sulfur.dioxide 1 527.35 2516.5
## - chlorides 1 531.53 2526.6
## - total.sulfur.dioxide 1 532.72 2529.4
## - sulphates 1 545.03 2558.7
## - volatile.acidity 1 556.14 2584.5
## - alcohol 1 622.10 2727.8
##
## Step: AIC=2510.7
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 525.30 2509.5
## <none> 524.97 2510.7
## - free.sulfur.dioxide 1 527.47 2514.8
## - pH 1 528.76 2517.9
## - chlorides 1 532.39 2526.7
## - total.sulfur.dioxide 1 533.69 2529.8
## - sulphates 1 545.32 2557.3
## - volatile.acidity 1 557.78 2586.2
## - alcohol 1 622.92 2727.5
##
## Step: AIC=2509.52
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 525.30 2509.5
## - free.sulfur.dioxide 1 528.19 2514.5
## - pH 1 528.86 2516.1
## - chlorides 1 533.66 2527.7
## - total.sulfur.dioxide 1 534.89 2530.7
## - sulphates 1 545.37 2555.5
## - volatile.acidity 1 565.36 2601.5
## - alcohol 1 625.08 2729.9
## Start: AIC=2517.3
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 525.22 2515.3
## - density 1 525.25 2515.4
## - residual.sugar 1 525.43 2515.8
## - citric.acid 1 525.68 2516.4
## <none> 525.21 2517.3
## - free.sulfur.dioxide 1 526.18 2517.7
## - pH 1 527.89 2521.8
## - total.sulfur.dioxide 1 532.50 2532.9
## - chlorides 1 536.19 2541.7
## - volatile.acidity 1 550.12 2574.6
## - sulphates 1 551.46 2577.7
## - alcohol 1 560.40 2598.2
##
## Step: AIC=2515.31
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 525.26 2513.4
## - residual.sugar 1 525.45 2513.9
## - citric.acid 1 525.71 2514.5
## <none> 525.22 2515.3
## - free.sulfur.dioxide 1 526.21 2515.7
## - pH 1 530.89 2527.1
## - total.sulfur.dioxide 1 533.03 2532.2
## - chlorides 1 536.95 2541.6
## - volatile.acidity 1 550.18 2572.7
## - sulphates 1 551.87 2576.6
## - alcohol 1 574.28 2627.5
##
## Step: AIC=2513.42
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 525.45 2511.9
## - citric.acid 1 526.08 2513.4
## <none> 525.26 2513.4
## - free.sulfur.dioxide 1 526.26 2513.8
## - pH 1 530.99 2525.3
## - total.sulfur.dioxide 1 533.08 2530.3
## - chlorides 1 537.10 2539.9
## - volatile.acidity 1 552.53 2576.2
## - sulphates 1 552.80 2576.8
## - alcohol 1 615.49 2714.2
##
## Step: AIC=2511.87
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 526.18 2511.6
## <none> 525.45 2511.9
## - free.sulfur.dioxide 1 526.55 2512.5
## - pH 1 531.22 2523.8
## - total.sulfur.dioxide 1 533.14 2528.5
## - chlorides 1 537.18 2538.1
## - volatile.acidity 1 552.57 2574.2
## - sulphates 1 552.91 2575.0
## - alcohol 1 616.79 2714.9
##
## Step: AIC=2511.64
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 526.18 2511.6
## - free.sulfur.dioxide 1 527.60 2513.1
## - pH 1 531.39 2522.2
## - total.sulfur.dioxide 1 534.85 2530.6
## - chlorides 1 539.00 2540.4
## - sulphates 1 552.97 2573.2
## - volatile.acidity 1 555.90 2579.9
## - alcohol 1 617.53 2714.4
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16